At least 24 hours before making the ice cream, place the bowl of the ice cream maker in the freezer.
Hull and quarter 6 ounces (about 1 cup) of strawberries; slice quarters crosswise into very thin pieces. In a mixing bowl, combine strawberries with ½ cup sugar and alcohol, and let stand in the refrigerator for at least 2 hours and up to 2 days.
Hull remaining strawberries and purée at high speed in a blender until very smooth, about 30 seconds. Strain through a fine-mesh strainer to remove all seeds and fibers, then measure and reserve 1 ½ cups of purée. Any extra purée can be put to another use.
In a clean mixing bowl, whisk together 1 ½ cups strawberry purée with half and half, corn syrup, and the remaining ¾ cup sugar until fully combined. Add salt to taste, and, if the mixture is too sweet, a few drops of lemon juice.
Chill in the freezer or an ice bath until the base is very cold, at least 45°F, then churn in an ice cream maker according to the manufacturer's instructions. In the last few minutes of churning, retrieve the strawberry pieces from the refrigerator, strain off the syrup, and add them to the churn. Transfer ice cream to an airtight container and chill in the freezer for at least 4 hours before serving. Yield: 1 quart.